Equation App

You can use the Equation app to solve simultaneous linear equations (two to six unknowns) and higher-order equations (2 to 6 degrees). It also has a Solver function that solves an equation for any variable.

Solving Simultaneous Linear Equations

Example: To solve the following equations for $x$ and $y$ ${\begin{matrix} 2 x - y = 5 \\ x ＋ 2 y = 10 \end{matrix}$

h > Equation

On the Type tab, select [Simultaneous] and then press > or O.

On the Unknowns tab, select the number of unknowns and then press > or O.

Here we have two unknowns, ( $x$ and $y$ ), so we choose [2 Unknowns].

On the Editor tab, input the coefficients of the equation.

2Es-(M)1E5E
1E2E10E

To solve the equations, press > or O.

This displays the solutions for $x$ and $y$ on the Result tab. Details about the values in the cell at the current cursor location are shown in the lower-right corner of the window.^*

When S > [‎ $\sqrt{} π$ ‎ Result] is turned on, display is in $\sqrt{}$ and $π$ form when possible (decimal form when not possible).
When S > [‎ $\sqrt{} π$ ‎ Result] is turned off, display is in decimal form only.

Note

The message “Infinitely Many Solutions” is displayed when there are infinite solutions.

The calculator uses inverse matrix $M$ ^-1 of coefficient matrix $M$ to solve a linear system of equations. Because of this, accuracy may suffer as determinant Det( $M$ ) of coefficient matrix $M$ approaches 0.

Solving Higher-Order Equations

Example: To solve $x^{2} + 2 x - 2 = 0$

h > Equation

On the Type tab, select [Polynomial] and then press > or O.

On the Degree tab, select the degree of the equation and then press > or O.

Since we are solving a quadratic equation, we select [a₂X²+a₁X+a₀=0] here.

On the Editor tab, input the coefficients of the equation.

1E2Es-(M)2E

To solve the equation, press > or O.

This displays the solution for $x$ on the Result tab. Details about the values in the cell at the current cursor location are shown in the lower-right corner of the window.^*

When S > [‎ $\sqrt{} π$ ‎ Result] is turned on, display is in $\sqrt{}$ and $π$ form when possible (decimal form when not possible). When S > [‎ $\sqrt{} π$ ‎ Result] is turned off, display is in decimal form.

Note

If the equation has multiple solutions, the number of solutions is displayed to the right of the solution.

Example: Solution of $x^{3} + 3 x^{2} + 3 x + 1 = 0$

Higher-order equation calculations may not produce accurate results or cause an error when the equation has multiple solutions.

If the equation has an imaginary solution, the solution is displayed in the form specified by the S > [Complex Mode] setting.

S key operation is ignored on the Result tab. Operate the S key on the Editor tab.

Using Solver

You can find the value of any variable in the equation without having to solve the equation by transforming or organizing the equation.

Example: Suppose an object is thrown into the air with initial velocity V and reaches height H after T time. Use the equation below to determine initial velocity V when H = 14 (m) and T = 2 (seconds), and gravitational acceleration G = 9.8 (m/s²).

$H = V T - {\frac{1}{2} G T}^{2}$

h > Equation

On the Type tab, select [Solver] and then press > or O.

On the Setup tab, enter the equation into the Eq line.

H = VT -e1d2r GT i

Press O.

This displays a list of variables included in the equation.

Specify for which of the variables you want to solve.

Press O to display the Solve for dialog.
To obtain initial speed V, select [V] and then press O.

Sequentially input H=14, T=2, and then G=9.8.

14E0E^*2E9.8E

The value to be solved for is the initial estimate value. Here, the initial estimated value is 0.

In the “Upper=‎” and “Lower=‎” lines, input the upper and lower limits of the desired solution, if necessary.

Press >. Or select and then press O.

This displays the calculation results on the Result tab.

“Lft=‎” and “Rgt=‎” are the calculated results of the left side and right side with the obtained result.

Note

$x$ and X are treated as the same variable.

If you input an expression without “=” in the “Eq” line in step 3, “expression = 0” is assumed.

Functions registered with the Graph&Table app can be input into the “Eq” line. Select T > [Recall], highlight the function you want to enter, and then press O.

Solver uses Newton’s method of approximation to find solutions. “Lft=‎” and “Rgt=‎” values are displayed because calculation using Newton’s method may produce an error with respect to the true solution. The closer the difference between the values of “Lft=‎” and “Rgt=‎” gets to 0, the smaller the error in the calculation results.

The Buttom_Continue button appears on the display when the calculator judges that convergence is not sufficient for the displayed results.

Solver obtains only one solution. For information about obtaining multiple solutions of a higher-order equation (such as $a x^{2} + b x + c = 0$ ), see Solving Higher-Order Equations.